Peculiarities of Raman Scattering by Polaritons and Polar Optical Phonons in Anisotropic Crystals

Strizhevskiǐ, V. L.; Yashkir, Yu. N.

doi:10.1002/pssb.2220610132

Cited by 12 publications

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“…The cubic susceptibility contribution into scattering is -y = e . It is connected with the Raman intensity tensor components aim by the equations6: eci 7jjmn(W , wr)eeerer = aimeeajnee (5) The nain values of dielectric function and the components of quadratic and cubic susceptibilities are complex…”

Section: Gain Factor For Scatteringby Nonordinary (Anisotropic) Polmentioning

confidence: 99%

Nonlinear response function for anisotropic polaritons in an orthorhombic crystal

Laptinskaya

Penin

1999

SPIE Proceedings

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In this article we consider the intensity distribution of the light scattering by anisotropic (nonordinary) polaritons in the wave number -wave vector coordinates. We propose formulae for polariton spectra numerical calculation which are adequate for any wave vector direction and for resonant and nonresonant frequency areas. The case of polariton branch splitting along the wave vector coordinate when this vector directs close to optical axis of orthorhombic crystal is discussed as an illustration of the method availability. Keywords: light scattering by polaritons, Raman scattering, infrared optics 1. POLARITON SPECTRA OF ORDINARY POLARITONS The spontaneous light scattering by polaritons (PS) is also called small-angle Raman scattering. In the process of spontaneous light scattering by polaritons in a nonlinear crystal without center of symmetry, laser (pumper) wave with wavenumber ill decays into signals waves (wide continious range of wavenumbers v,) and idler, or polariton ( v = LIj -z.') waves. Polariton wavelengths are in infrared range. Vectors of interacting waves make the triangle: k1=k+k(1) Angles i9 between k1 and k are small, and values of k are almost equal to wave vectors of infrared light waves. PS spectroscopy not only combines advantages and possibilities of Raman and infrared (IR) spectroscopy methods but also contains additional information and is more sensitiveThe main difference of the PS spectrum from the Raman one is that the intensity P(zi, Ic) is the function frofri two coordinates, wavenumber and wavevector k = Iki . The wave vectors k actual range in eq. (1) may be wide.It corresponds to scattering angles t9 from zero to maximum value, which is defined by the optical elements and height of spectrograph sleet and is usually of 4 -120 . The points which correspond to the peaks of wave vector (or angular) line shapes P(k) at given wavenumbers ii we will call polariton modes k. The curve ii(k) connecting these peaks on the ii -k plane is called here a polariton mode curve. The area where P(k) is not less then 1% from peak value is called a polaritorz branch.If polariton waves are transversely polarized, the scattering intensity is defined by the nonlinear response function being proportional to gain factor1 G: P(u, ) G = Im(4irD2 + 0) = Im[4ir2/(jt2 -6*) + 8] (2) Here spectrum coordinates are wavenumber ii and = fkI/v. Formula contains complex values of dielectric function 6, qudratic x and cubic ® susceptibilities. The inverse wave vector mismatch function D = (p2 _ describes an area of the infrared equilibrium fluctuations existence on the ii -p plane (the polariton branch) . From twodimensional PS spectra it is possible to obtain information about the phonons dynamic parameters, that is, about their contributions into linear, quadratic and cubic susceptibilities and damping constant. The method of dynamic parameters correct calqulation from intensity distribution have been rather well developed now, but only for the case when polariton wave is ordinary, that is, transverse polarized24. 2....

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Section: Gain Factor For Scatteringby Nonordinary (Anisotropic) Polmentioning

confidence: 99%

Nonlinear response function for anisotropic polaritons in an orthorhombic crystal

Laptinskaya

Penin

1999

SPIE Proceedings

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Theoretical Treatment of Nonstationary Scattering by Phonons and Polaritons Part I. Derivation of the Basic Equations

Ponath¹,

Schubert²

1976

Annalen der Physik

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A b s t r a c t . The equations of motion of a two-level system and a harmonic oscillator coupled to a dissipative system are discussed; the dissipative system is assumed to consist of a large number of radiation oscillators. Special equations for the determination of the correlation functions of the fluctuation forces are derived under the condition of large time values, for which the atomic system has "forgotten" its initial state. The expectation values of the correlation functions are connected with the damping constant and the population operator of the excited state of the atomic system is in thermal equilibrium. Taking into account the influence of the coherent radiation field on the atomic system, the basic equations for the treatment of the nonstationary Raman scattering by polaritons are derived; the temporal range of validity is discussed.Using a time-dependent "variable" Fourier transformation, the nonstationary time-and spacedependent spectral densities are related to the correlation functions of the fields; here the Wiener-Khintchine theorem is applied in a nonstationary form. The limiting cases of the stationary scattering process as well as the usually introduced correlators of the slowly varying amplitudes are discussed.Theoretische Behandlung nichtstationiirer Streuprozesse an Phononen und Polaritonen. I. Ableitung der Grundgleichung I n ha1 tsverzeic hnis. Es werden die Heisenbergschen Operatorbewegungsgleichungen fur ein Zweiniveausystem und den harmonischen Oszillator bei Ankopplung des atomaren an ein durch ein Strahlungsfeld konkretisiertes dissipatives System aufgestellt. Die Korrelationsfunktionen der Fluktuationsoperatoren werden fur das thermische Gleichgewicht (Temperatur T) zwischen beiden Systemen bei Zeiten, die groB gegen die Relaxationszeit P1 sind, berechnet; sie bestimmen sich aus dem Energieerwartungswert des atomaren Systems und sind bei der Annahme einer glatten Modendichte fur das dissipative Strahlungsfeld zeitlich deltakorreliert. Mit Ar&opplung des kohlrenten Systems werden die nichtstationaren Grundgleichungen fur Feld-und Materieoperatoren zur Ramanstreuung an Polaritonen unter Berucksichtigung der Materiefluktuationen aufgestellt und ihr zeitlicher Gultigkeitsbereich abgegrenzt.Unter Verwendung von zeitabhlngigen ,,laufenden" Fouriertransformationen werden uber ein nichtstationares Analogon zum Wiener-Chintschin-Theorem die nichtstationaren zeit-und ortsabhangigen Spektraldichten pro Frequenz-und Raumwinkelelement in Zusammenhang mit den Korrelationsfunktionen der Felder gebracht. Der Ubergang zum stationiiren Streufall sowie der Zusammenhang der SpektralgroBen mit den ublicherweise eingefuhrten Korrelatoren der ,,langsamen" Feldamplitnden werden diskutiert.

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The theory of Raman scattering by surface polaritons

Strizhevskiǐ¹,

Yashkir²

1975

Physica Status Solidi (b)

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The fluctuation-dissipation theory of spontaneous Raman scattering (RS) by surface polaritons (SP) is carried out. The appearance of scattering emission is treated as the result of mixing of the pump emission and the fluctuating surface electromagnetic field. A calculation is made of the surface electromagnetic fluctuations near the interface between the two dissipative media and in the absorbing layer surrounded by transparent dielectrics. Expressions are found and analysed describing the frequency-angular distribution of the scattering emission intensity in the layer, taking into account the interference of SP localized near different surfaces (and near the interface of two absorbing media). The RS intensities are expressed by the phenomenological parameters of the media. It is also shown that the RS intensity decreases essentially with increasing scattering angle 0 (when the scattering frequency approaches the frequency of the surface phonon) due to the increasing localieation of SP. Various essential physical features of the phenomenon are analysed in detail: scattering line shape and its angular dependence; the B'ermi resonance of SP and its display in the RS; mixing of SP of different media and RS by appearing mixed modes; RS by SP connected genetically with the linear medium which borders with the transparent nonlinear medium; evolution of RS in a layer by decreasing its thickness, and others.

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Peculiarities of Raman Scattering by Polaritons and Polar Optical Phonons in Anisotropic Crystals

Cited by 12 publications

References 10 publications

Nonlinear response function for anisotropic polaritons in an orthorhombic crystal

Nonlinear response function for anisotropic polaritons in an orthorhombic crystal

Theoretical Treatment of Nonstationary Scattering by Phonons and Polaritons Part I. Derivation of the Basic Equations

The theory of Raman scattering by surface polaritons

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